Will a chin implant make my face look more 'square'? (photo)

You have a few options to improve your chin and profile. If you’re not sure you’re ready for surgery, but still want to improve and strengthen your chin and profile, I’d suggest augmenting your chin with Sculptra and/or Voluma. I’d also remove the fat underneath your chin with liposuction or Kybella. If you like your new look, you can make it permanent with a chin implant.

Based on these photos (without full face photos showing your nose) I do not think that chin augmentation would address your problem. Your chin seem to be within acceptable relationship with lower face, lips and nose tip (as much as one can see). Conservative liposuction of the neck and along jawline may be a other option? In person evaluation is needed for more accurate plan of treatment. Good luck.

With a vertically short chin/lower jaw, the proper approach to making your face less square/round is to lengthen it. This can be done. by a chin implant but it has to be a special vertical lengthening one to do so. It can also be done by an opening wedge intraoral bony genioplasty.

 Hi, I have performed many facial shaping procedures using dermal fillers, silastic facial implants (cheek, chin, lips), liposuction and/or facelifts for over 30 years.  From the photos, your cheeks are flat in the front, there is a slight amount of excess fat in front of and below the cheeks however the chin is "not" weak.  Your face is currently rectangularly shaped.
 You can compare "your profile" to the ones in the attached video who underwent chin augmentation with a silastic chin implant to correct a weak chin.  In your case, a chin implant would over-project your chin making the face very masculine and out of balance.   
 Following my beauty principles, women look the most feminine, youthful and attractive with heart shaped faces.  Heart shaped faces have cheeks that are full and round in the front.  When the cheeks are flat or concave, Cheek augmentation with a dermal filler or using cheek implants for a permanent enhancement will create full, round cheeks that will feminize the entire face.  Liposuction to reduce the slight amount of excess fat can be performed to further shape the cheeks and face.
Hope this helps.